Utah’s Mia Love hasn’t exactly announced that she is running for Congress again, but Rep. Jim Matheson isn’t taking any chances.

Mr. Matheson, a Democrat who barely survived a challenge from Mrs. Love, a Republican, in 2012, is building a war chest in anticipation of another duel, raising $288,000 in the first quarter of 2013, which gives him $241,000 cash on hand.

Meanwhile, Mrs. Love, who filed a statement of candidacy in March but says she hasn’t made a final decision, lists $147,000 in her campaign account after collecting $44,300 in the period ending March 31, according to Federal Election Commission reports filed Monday.

Mrs. Love, the mayor of Saratoga Springs, lost by just 768 votes in November, coming closer than any previous Republican to picking off the resilient Mr. Matheson, Utah’s only Democratic House member. Her unusual background as a black, Brooklyn, N.Y.,-born, Haitian-American Mormon helped make her a rising star in the GOP during the campaign. She was given a plum speaking slot at the party’s 2012 Tampa, Fla., nominating convention and her political future remains a subject of intense national scrutiny.

But Mr. Matheson, who began his seventh term in Congress in January, has shown himself to be an incredibly tough out, said Kirk Jowers, director of the Hinckley Institute of Politics at the University of Utah.

“Mia Love discovered what most politicos in Utah already knew, which is that Jim Matheson is a phenomenal candidate,” Mr. Jowers said. “He does all the little things well he’s tremendous at get-out-the-vote.”

At the same time, “Jim Matheson certainly learned that Mia Love is a formidable candidate she can raise funds and get national attention,” he said. “So it seems inevitable that there would be a rematch between these two.”

Certainly Mrs. Love is acting like a candidate. She has been popping up as a panelist on television news shows, and in March delivered a prime-time speech at the annual Conservative Political Action Conference.

“We haven’t made a formal decision we want to make sure we have enough behind it,” she told The Washington Times.

She has hired Utah political operative Dave Hansen, the longtime campaign manager for Sen. Orrin G. Hatch, Utah Republican, who is widely regarded as the best in the state.

Mrs. Love may be the last Republican any Democrat wants to face CPAC emcee Steven Crowder called her the candidate “liberals check under their bed for.” Young and telegenic, her background and status as a rare black Republican woman candidate upend political stereotypes.

Some analysts say the road to victory would be more difficult for her in 2014. In 2012, she was able to ride the coattails of Republican presidential candidate Mitt Romney, a Mormon who enjoyed enormous popularity in Utah.

Off-year elections tend to favor the party that doesn’t hold the White House. If she were to run in 2014, Mrs. Love also wouldn’t be an unknown commodity like she was in 2012.

“I think it would be easier than starting from zero,” Mrs. Love said. “People didn’t know where Saratoga Springs was, let alone who I was.”

Mr. Matheson is also seen as a possible Democratic candidate for Senate or governor, but not until 2016.

The National Republican Campaign Committee already is targeting the 2014 House race with an online ad calling the Democrat “out of touch.”

Mr. Matheson has used the early opposition to drum up fundraising support. “This one was critical with outside groups already targeting our race and opponents lining up,” he said in an email to donors, according to The Salt Lake Tribune.

“He leaves nothing to chance. But Mia Love is very interesting,” Mr. Jowers said. “If Matheson could pick anyone other than Mia Love to run against, I think he’d pick curtain No. 2.”